Eliminating the pollution effect in Helmholtz problems by local subscale correction
Eliminating the pollution effect in Helmholtz problems by local subscale correction
dc.contributor.author | Peterseim, Daniel | |
dc.date.accessioned | 2024-08-21T13:34:10Z | |
dc.date.available | 2024-08-21T13:34:10Z | |
dc.date.issued | 11.2014 | |
dc.identifier.uri | https://hdl.handle.net/20.500.11811/11916 | |
dc.description.abstract | We introduce a new Petrov-Galerkin multiscale method for the numerical approximation of the Helmholtz equation with large wave number κ in bounded domains in ℝd. The discrete trial and test spaces are generated from standard mesh-based finite elements by local subscale correction in the spirit of numerical homogenization. The precomputation of the correction involves the solution of coercive cell problems on localized subdomains of size ℓH; H being the mesh size and ℓ being the oversampling parameter. If the mesh size and the oversampling parameter are such that Hκ and log(κ)/ℓ fall below some generic constants and if the cell problems are solved sufficiently accurate on some finer scale of discretization, then the method is stable and its error is proportional to H; pollution effects are eliminated in this regime. | en |
dc.format.extent | 29 | |
dc.language.iso | eng | |
dc.relation.ispartofseries | INS Preprints ; 1411 | |
dc.rights | In Copyright | |
dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | |
dc.subject.ddc | 510 Mathematik | |
dc.subject.ddc | 518 Numerische Analysis | |
dc.title | Eliminating the pollution effect in Helmholtz problems by local subscale correction | |
dc.type | Preprint | |
dc.publisher.name | Institut für Numerische Simulation (INS) | |
dc.publisher.location | Bonn | |
dc.rights.accessRights | openAccess | |
dc.relation.doi | https://doi.org/10.1090/mcom/3156 | |
ulbbn.pubtype | Zweitveröffentlichung | |
dcterms.bibliographicCitation.url | https://ins.uni-bonn.de/publication/preprints |
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